Current Research on Mathematical Inequalities II

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 30 June 2024 | Viewed by 6218

Special Issue Editor

Department of Mathematics, Université de Caen, LMNO, Campus II, Science 3, 14032 Caen, France
Interests: mathematical statistics; applied statistics; data analysis; probability; applied probability; analytic inequalities
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The subject of mathematical inequalities has always fascinated mathematicians, and is still the subject of numerous research articles. Mathematical inequalities can be self-sufficient, or be key parts of proofs of important theorems in all branches of mathematics. Inequalities are essential to mathematics; thus, any advancements in this area are welcome.

The recent success of the Special Issue "Current Research on Mathematical Inequalities" published in Axioms is proof of this. On this solid foundation, Axioms offers a new research space on mathematical inequalities, entitled "Current Research on Mathematical Inequalities II". The objective is to compile cutting-edge research the most recent advances regarding various types of mathematical inequality. Inequalities that are purely mathematical, applied mathematical, or based on strong conjecture are all acceptable. Only papers that are flawlessly written, organized, and contain novel research findings will be taken into consideration.

The following are just a few examples of the research topics considered in this Special Issue: conjectural inequalities with numerical evidence; inequalities in analysis (sophisticated or not, with special functions or not, applied or not); inequalities in approximation theory; inequalities in combinatorics; inequalities in economics; inequalities in geometry; inequalities in mechanics; inequalities in number theory;  inequalities in optimization; inequalities in physics; inequalities in probability; and inequalities in statistics.

Dr. Christophe Chesneau
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • inequalities in theoretical mathematics
  • inequalities in applied mathematics
  • inequalities in physics
  • inequalities in probability and statistics
  • conjectural inequality with numerical evidence

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Published Papers (8 papers)

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Research

25 pages, 336 KiB  
Article
Fundamental Properties of Muckenhoupt and Gehring Weights on Time Scales
Axioms 2024, 13(2), 98; https://doi.org/10.3390/axioms13020098 - 31 Jan 2024
Viewed by 740
Abstract
Some fundamental properties of the Muckenhoupt class Ap of weights and the Gehring class Gq of weights on time scales and some relations between them will be proved in this paper. To prove the main results, we will apply an approach [...] Read more.
Some fundamental properties of the Muckenhoupt class Ap of weights and the Gehring class Gq of weights on time scales and some relations between them will be proved in this paper. To prove the main results, we will apply an approach based on proving some properties of integral operators on time scales with powers and certain mathematical relations connecting the norms of Muckenhoupt and Gehring classes. The results as special cases cover the results for functions following David Cruz-Uribe, C. J. Neugebauer, and A. Popoli, and when the time scale equals the positive integers, the results for sequences are essentially new. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities II)
14 pages, 298 KiB  
Article
Improvements of Integral Majorization Inequality with Applications to Divergences
Axioms 2024, 13(1), 21; https://doi.org/10.3390/axioms13010021 - 28 Dec 2023
Viewed by 745
Abstract
Within the recent wave of research advancements, mathematical inequalities and their practical applications play a notably significant role across various domains. In this regard, inequalities offer a captivating arena for scholarly endeavors and investigational pursuits. This research work aims to present new improvements [...] Read more.
Within the recent wave of research advancements, mathematical inequalities and their practical applications play a notably significant role across various domains. In this regard, inequalities offer a captivating arena for scholarly endeavors and investigational pursuits. This research work aims to present new improvements for the integral majorization inequalities using an interesting aproach. Certain previous improvements have been achieved for the Jensen inequality as direct outcomes of the main results. Additionally, estimates for the Csiszár divergence and its cases are provided as applications of the main results. The circumstances under which the principal outcomes offer enhanced estimations for majorization differences are also underscored and emphasized. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities II)
13 pages, 286 KiB  
Article
Generalized Refinements of Reversed AM-GM Operator Inequalities for Positive Linear Maps
Axioms 2023, 12(10), 977; https://doi.org/10.3390/axioms12100977 - 17 Oct 2023
Viewed by 680
Abstract
We shall present some more generalized and further refinements of reversed AM-GM operator inequalities for positive linear maps due to Xue’s and Ali’s publications. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities II)
13 pages, 284 KiB  
Article
Equivalent Statements of Two Multidimensional Hilbert-Type Integral Inequalities with Parameters
Axioms 2023, 12(10), 956; https://doi.org/10.3390/axioms12100956 - 10 Oct 2023
Viewed by 546
Abstract
By means of the weight functions, the idea of introduced parameters and the transfer formulas, two multidimensional Hilbert-type integral inequalities with the general nonhomogeneous kernel as [...] Read more.
By means of the weight functions, the idea of introduced parameters and the transfer formulas, two multidimensional Hilbert-type integral inequalities with the general nonhomogeneous kernel as H(||x||αλ1||y||βλ2)(λ1,λ20) are given, which are some extensions of the Hilbert-type integral inequalities in the two-dimensional case. Some equivalent conditions of the best value and several parameters related to the new inequalities are provided. Two corollaries regarding the kernel, represented as kλ(||x||αλ1,||y||βλ2)(λ1,λ20), are given, and a few new inequalities for the particular parameters are obtained. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities II)
20 pages, 346 KiB  
Article
Innovative Interpolating Polynomial Approach to Fractional Integral Inequalities and Real-World Implementations
Axioms 2023, 12(10), 914; https://doi.org/10.3390/axioms12100914 - 26 Sep 2023
Viewed by 1096
Abstract
Our paper explores Hermite–Hadamard inequalities through the application of Abel–Gontscharoff Green’s function methodology, which involves interpolating polynomials and Riemann-type generalized fractional integrals. While establishing our main results, we explore new identities. These identities are used to estimate novel findings for functions, such that [...] Read more.
Our paper explores Hermite–Hadamard inequalities through the application of Abel–Gontscharoff Green’s function methodology, which involves interpolating polynomials and Riemann-type generalized fractional integrals. While establishing our main results, we explore new identities. These identities are used to estimate novel findings for functions, such that the second derivative of the functions is monotone, absolutely convex, and concave. A section relating the results of exploration to generalized means and trapezoid formulas is included in the applications. We anticipate that the method presented in this study will inspire further research in this field. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities II)
17 pages, 346 KiB  
Article
Derivation of Bounds for Majorization Differences by a Novel Method and Its Applications in Information Theory
Axioms 2023, 12(9), 885; https://doi.org/10.3390/axioms12090885 - 16 Sep 2023
Cited by 1 | Viewed by 742
Abstract
In the recent era of research developments, mathematical inequalities and their applications perform a very consequential role in different aspects, and they provide an engaging area for research activities. In this paper, we propose a new approach for the improvement of the classical [...] Read more.
In the recent era of research developments, mathematical inequalities and their applications perform a very consequential role in different aspects, and they provide an engaging area for research activities. In this paper, we propose a new approach for the improvement of the classical majorization inequality and its weighted versions in a discrete sense. The proposed improvements give several estimates for the majorization differences. Some earlier improvements of the Jensen and Slater inequalities are deduced as direct consequences of the obtained results. We also discuss the conditions under which the main results give better estimates for the majorization differences. Applications of the acquired results are also presented in information theory. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities II)
20 pages, 321 KiB  
Article
On Further Refinements of Numerical Radius Inequalities
Axioms 2023, 12(9), 807; https://doi.org/10.3390/axioms12090807 - 22 Aug 2023
Cited by 2 | Viewed by 550
Abstract
This paper introduces several generalized extensions of some recent numerical radius inequalities of Hilbert space operators. More preciously, these inequalities refine the recent inequalities that were proved in literature. It has already been demonstrated that some inequalities can be improved or restored by [...] Read more.
This paper introduces several generalized extensions of some recent numerical radius inequalities of Hilbert space operators. More preciously, these inequalities refine the recent inequalities that were proved in literature. It has already been demonstrated that some inequalities can be improved or restored by concatenating some into one inequality. The main idea of this paper is to extend the existing numerical radius inequalities by providing a unified framework. We also present a numerical example to demonstrate the effectiveness of the proposed approach. Roughly, our approach combines the existing inequalities, proved in literature, into a single inequality that can be used to obtain improved or restored results. This unified approach allows us to extend the existing numerical radius inequalities and show their effectiveness through numerical experiments. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities II)
11 pages, 294 KiB  
Article
A Generalized Convexity and Inequalities Involving the Unified Mittag–Leffler Function
Axioms 2023, 12(8), 795; https://doi.org/10.3390/axioms12080795 - 17 Aug 2023
Cited by 1 | Viewed by 574
Abstract
This article aims to obtain inequalities containing the unified Mittag–Leffler function which give bounds of integral operators for a generalized convexity. These findings provide generalizations and refinements of many inequalities. By setting values of monotone functions, it is possible to reproduce results for [...] Read more.
This article aims to obtain inequalities containing the unified Mittag–Leffler function which give bounds of integral operators for a generalized convexity. These findings provide generalizations and refinements of many inequalities. By setting values of monotone functions, it is possible to reproduce results for classical convexities. The Hadamard-type inequalities for several classes related to convex functions are identified in remarks, and some of them are also presented in last section. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities II)
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